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We show that phononic frequency conversion can be enhanced by orders ofmagnitude in piezoelectric systems by heterogeneous integration ofhigh-mobility semiconductor films. A lithium niobate and indium galliumarsenide heterostructure is utilized to demonstrate efficient three-wave mixingprocesses at microwave frequencies, including 16% phononic power conversionefficiency for sum-frequency generation and 1% phononic power conversionefficiency for difference-frequency generation, as well as the most efficientdegenerate four-wave phononic mixing to date. We present a theoretical modelthat accurately predicts the sum-frequency and difference-frequency generationprocesses and we show that the conversion efficiency can be further enhanced bythe application of semiconductor bias fields. Laser Doppler vibrometry is thenapplied to examine many three-wave and four-wave mixing processessimultaneously in the same device. Through the use of our developed model, weshow that these nonlinearities can be enhanced far beyond what is demonstratedhere by confining phonons to smaller dimensions in waveguides and optimizingsemiconductor material properties or using 2D semiconductors.

High-Efficiency Three-Wave and Four-Wave Phonon Mixing Via Electron-Mediated Nonlinearity in Semiconductor-Piezoelectric Heterostructures